Penninn Eymundsson Skólavörðustíg: I like books and I like bookshops. This was an amazing place to window shop for a while and explore some local authors. If you are interested in exploring some Icelandic writers, you can check out Audur Ava Olafsdottir, Andri Snaer Magnason, Jon Kalman Stefansson or Sjon.
Pride of Iceland: Iceland is a highly costly country in general and it also affects the prices for souvenirs. If you cannot leave a country without buying a bunch of magnets for yourself or your family, a mug or a gift like that, Pride of Iceland is your place. Compared to all other places, the price is almost the half and you can find pretty items the same.
WHERE TO EAT
IKEA: In the end of our driving tour in Snaefellsnes peninsula, we drove to Reykjavik. Before reaching our airbnb destination to spend the night, we decided that we were bored of cooking on ourselves as we did in the past week to save some money. With the desire to have a dinner out, we decided to go to IKEA. Having a dinner in IKEA was indeed an amazing idea, because we didn't have to think about parking, we didn't have to think about how much to spend - obviously the prices are similar to the international market and we didn't have to think about what to eat - you can opt for traditional Icelandic lamb or just regular Swedish meatballs. Even if alcoholic drinks are mostly expensive in Iceland in general, a can of beer costs about 100ISK, which is not that expensive at all. In total, it was a really good and affordable dinner destination.
Cafe Babalu: In the morning, we decided to have a breakfast out and found this little cute bar. It's really in the center and super close to the Laugavegur Street, so you might come by at any time. The prices are nice, they serve pretty good home made muffins and cakes for breakfast but also sandwiches, pancakes or soup. You can get a refill coffee if you order the black coffee once - I took almost 6 amazing cups to compensate the days I've spent without coffee breaks. It was the best coffee ever.

Baejarins Beztu Pylsur: This is a small hotdog stand, where you can buy only hotdogs from. You don't have much choice, you can only select what to have inside the hotdog but it's quite delicious.
It turns out, in 2004, Bill Clinton decided to have a quick bite here and soon it became a popular spot. Soon, the Guardian announced the place as the best hot dog stand in Europe. Since then, many tourists and celebrities kept going for a bite. The price is good - only 2 euros for a hot dog - and it really is delicious! Expect waiting almost half an hour to order and not finding a seat as you enjoy your food.
Even though I didn't taste it, the second best alternative for a tasty hot dog bite is the Biarni Fel. It is pretty close to Baejarins Beztu Pylsur, so you can simply try both of them and make your own experimentation.

Icelandic Street Food: There are two things you cannot leave Iceland without eating: the rotten shark and the sea food soup. We were lucky to find the shark museum in the Snaefelssnes penisula and not in Reykjavik, it was the time to taste some soup. Actually you can find it in almost every restaurant, but we were searching for the best one - and we found it!
After not getting full by a small hot dog, we decided to find an alternative for lunch and headed to the Icelandic Street Food.
I was hoping to eat more hot dogs, but it turns out here they are only making home made Icelandic food from their granny recipes. Let me tell you that the prices are not that cheap, but the place works with the refill concept, so once you order a dish, you can keep refilling your cup until you say "well, I ate enough for 3 days!"
I have tasted the soup with the shellfish and the lamb, I totally prefer the sea food version. In fact, we ate so much here for late lunch, we completely passed dinner.
The music is amazing and the owner is really friendly - they gave us also tickets for free beers in the bar next door. If you take one advice from this post, eat here.